On the Brink of Paradox : Highlights from the Intersection of Philosophy and Mathematics

Agustin Rayo

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Language: English

Published by MIT Press Ltd Apr 2019, 2019

0262039419 / 9780262039413

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Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH

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Neuware - An introduction to awe-inspiring ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, and computability theory.This book introduces the reader to awe-inspiring issues at the intersection of philosophy and mathematics. It explores ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, computability theory, the Grandfather Paradox, Newcomb's Problem, the Principle of Countable Additivity. The goal is to present some exceptionally beautiful ideas in enough detail to enable readers to understand the ideas themselves (rather than watered-down approximations), but without supplying so much detail that they abandon the effort. The philosophical content requires a mind attuned to subtlety; the most demanding of the mathematical ideas require familiarity with college-level mathematics or mathematical proof.The book covers Cantor's revolutionary thinking about infinity, which leads to the result that some infinities are bigger than others; time travel and free will, decision theory, probability, and the Banach-Tarski Theorem, which states that it is possible to decompose a ball into a finite number of pieces and reassemble the pieces so as to get two balls that are each the same size as the original. Its investigation of computability theory leads to a proof of Gödel's Incompleteness Theorem, which yields the amazing result that arithmetic is so complex that no computer could be programmed to output every arithmetical truth and no falsehood. Each chapter is followed by an appendix with answers to exercises. A list of recommended reading points readers to more advanced discussions. The book is based on a popular course (and MOOC) taught by the author at MIT.…

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Title
On the Brink of Paradox : Highlights from the Intersection of Philosophy and Mathematics
Author
Agustin Rayo
Publisher
MIT Press Ltd Apr 2019
Publication year
2019
Condition
Neu
Binding
Buch
Language
English
ISBN 10
0262039419
ISBN 13
9780262039413
Item weight
652 grams
Dimensions
236x181x25 mm

AHA-BUCH GmbH

Einbeck, Germany

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AbeBooks seller since August 14, 2006

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